平方根螺旋的几何构造与动态演示

GeoGebra 命令及参数

1. Intersect(xAxis, yAxis) → A
2. Circle(B, a) → c
3. Segment(A, B) → f
4. OrthogonalLine(B, f) → g
5. Intersect(c, g) → C, D
6. Segment(A, D) → h
7. Circle(D, a) → d
8. OrthogonalLine(D, h) → i
9. Intersect(d, i) → E, F
10. Segment(A, F) → j
11. Circle(F, a) → e
12. OrthogonalLine(F, j) → k
13. Intersect(e, k) → G, H
14. Segment(A, H) → l
15. Circle(H, a) → p
16. OrthogonalLine(H, l) → m
17. Intersect(p, m) → I, J
18. Segment(J, A) → n
19. OrthogonalLine(J, n) → q
20. Circle(J, a) → r
21. Intersect(r, q) → K, L
22. Segment(K, A) → s
23. Circle(K, a) → t
24. OrthogonalLine(K, s) → b
25. Intersect(t, b) → M, N
26. Segment(M, A) → f_1
27. Circle(M, a) → c_1
28. OrthogonalLine(M, f_1) → g_1
29. Intersect(c_1, g_1) → O, P
30. Segment(O, A) → h_1
31. Circle(O, a) → d_1
32. OrthogonalLine(O, h_1) → i_1
33. Intersect(d_1, i_1) → Q, R
34. Segment(Q, A) → j_1
35. Circle(Q, a) → e_1
36. OrthogonalLine(Q, j_1) → k_1
37. Intersect(e_1, k_1) → S, T
38. Segment(S, A) → l_1
39. Circle(S, a) → p_1
40. OrthogonalLine(S, l_1) → m_1
41. Intersect(p_1, m_1) → U, V
42. Segment(U, A) → n_1
43. Line(A, B) → q_1
44. Circle(A, D) → r_1
45. Circle(A, F) → s_1
46. Circle(A, H) → t_1
47. Circle(A, J) → c_2
48. Circle(A, K) → d_2
49. Circle(A, M) → e_2
50. Circle(A, O) → f_2
51. Circle(A, Q) → g_2
52. Circle(A, S) → h_2
53. Circle(A, U) → k_2
54. Intersect(k_2, q_1) → W, Z
55. Intersect(h_2, q_1) → A_1, B_1
56. Intersect(g_2, q_1) → C_1, D_1
57. Intersect(f_2, q_1) → E_1, F_1
58. Intersect(e_2, q_1) → G_1, H_1
59. Intersect(d_2, q_1) → I_1, J_1
60. Intersect(c_2, q_1) → K_1, L_1
61. Intersect(t_1, q_1) → M_1, N_1
62. Intersect(s_1, q_1) → O_1, P_1
63. Intersect(r_1, q_1) → Q_1, R_1
64. CircleArc(A, R_1, D) → p_2
65. CircleArc(A, P_1, F) → q_2
66. CircleArc(A, N_1, H) → r_2
67. CircleArc(A, L_1, J) → s_2
68. CircleArc(A, J_1, K) → t_2
69. CircleArc(A, H_1, M) → c_3
70. CircleArc(A, F_1, O) → d_3
71. CircleArc(A, D_1, Q) → e_3
72. CircleArc(A, B_1, S) → f_3
73. CircleArc(A, Z, U) → g_3
74. Segment(D, B) → a_1
75. Segment(F, D) → b_1
76. Segment(H, F) → i_2
77. Segment(J, H) → j_2
78. Segment(K, J) → l_2
79. Segment(M, K) → m_2
80. Segment(O, M) → n_2
81. Segment(Q, O) → a_2
82. Segment(S, Q) → b_2
83. Segment(U, S) → h_3
84. Angle(D, B, A) → α
85. Angle(F, D, A) → β
86. Angle(H, F, A) → γ
87. Angle(J, H, A) → δ
88. Angle(K, J, A) → ε
89. Angle(M, K, A) → ζ
90. Angle(O, M, A) → η
91. Angle(Q, O, A) → θ
92. Angle(S, Q, A) → ι
93. Angle(U, S, A) → κ
94. Polygon(A, B, D) → t1, d_4, a_3, b_3
95. Polygon(A, D, F) → t2, f_4, a_4, d_5
96. Polygon(A, F, H) → t3, h_4, a_5, f_5
97. Polygon(A, H, J) → t4, j_3, a_6, h_5
98. Polygon(A, J, K) → t5, k_3, a_7, j_4
99. Polygon(A, K, M) → t6, m_3, a_8, k_4
100. Polygon(A, M, O) → t7, o, a_9, m_4
101. Polygon(A, O, Q) → t8, q_3, a_{10}, o_1
102. Polygon(A, Q, S) → t9, s_3, a_{11}, q_4
103. Polygon(A, S, U) → t10, u, a_{12}, s_4
104. Centroid(t1) → S_1
105. Centroid(t2) → T_1
106. Centroid(t3) → U_1
107. Centroid(t4) → V_1
108. Centroid(t5) → W_1
109. Centroid(t6) → Z_1
110. Midpoint(n_2) → A_2
111. Centroid(t7) → B_2
112. Centroid(t8) → C_2
113. Centroid(t9) → D_2
114. Centroid(t10) → E_2
115. Ray(A, B) → i_3